My bone is affecting vertices not assigned to it?
If you created the weights with automatic weights then mesh proximity is what determines the automatic weights. This is a common problem.
Do not depend on eyeball inspection of the problem area. You may not be able to see fine differences of color.  Paint it zero weight for the problem bone.
I suggest you add another bone for the neck to create more precision





Bones have many options, the Blender User can actually see the weights for a single vertex in the [edit mode] with display of weights enabled. See image above.  This is not a tutorial.  BSE may have other tutorials as well as the site that rhymes with noonoob.